Before stating our assumptions on \(\theta _i\)  and \(\varepsilon _{i, T}\) , we provide several examples of how \(\vartheta _{i, T}\)  may be constructed. Intuitively, \(\vartheta _{i, T}\)  are estimators of \(\theta _i\)  that have growing precision. \(\vartheta _{i, T}\)  can potentially be biased. Our setting nests the setup considered by [1]} and the typical setup of random effects meta-analysis (see e.g. [2]}).
